The theory of radicals in lattice-ordered rings

Special classes of associative lattice-ordered rings are introduced which are analogous to V. A. Andrunakievich's special classes of rings. The appropriate special radicals for them are defined. It is shown that the special classes of $l$-rings are: 1) the class of all $l$-primary $l$-rings; 2) the class of all $l$-primary $l$-rings without locally nilpotent $l$-ideals (it is shown that the corresponding $l$-ideal is a union of nil-$l$-ideals of the ring); 3) the class of $l$-rings not containing strictly positive divisors of zero; 4) the class of subdirectly indecomposable $l$-rings with $l$-idempotent core.